04850cam a2200529Ka 4500 ocn938788572 OCoLC 20190328114814.0 m o d cr cnu---unuuu 160212s2016 cau ob 001 0 eng d IDEBK eng pn IDEBK N$T YDXCP OPELS UIU OCLCF EBLCP CDX DEBSZ OCLCQ TEFOD OCLCQ IDB OCLCQ U3W MERUC D6H OCLCQ 940438495 0128047755 (electronic bk.) 9780128047750 (electronic bk.) 012804277X 9780128042779 (OCoLC)938788572 (OCoLC)940438495 QA377.3 MAT 005000 bisacsh MAT 034000 bisacsh 515.353 23 Zhou, Yong. Fractional evolution equations and inclusions / [electronic resource] Yong Zhou. San Diego, CA : Academic Press, �2016. 1 online resource text txt rdacontent computer c rdamedia online resource cr rdacarrier Print version record. Includes bibliographical references and index. Fractional evolution inclusions are an important form of differential inclusions within nonlinear mathematical analysis. They are generalizations of the much more widely developed fractional evolution equations (such as time-fractional diffusion equations) seen through the lens of multivariate analysis. Compared to fractional evolution equations, research on the theory of fractional differential inclusions is however only in its initial stage of development. This is important because differential models with the fractional derivative providing an excellent instrument for the description of memory and hereditary properties, and have recently been proved valuable tools in the modeling of many physical phenomena. The fractional order models of real systems are always more adequate than the classical integer order models, since the description of some systems is more accurate when the fractional derivative is used. The advantages of fractional derivatization become evident in modeling mechanical and electrical properties of real materials, description of rheological properties of rocks and in various other fields. Such models are interesting for engineers and physicists as well as so-called pure mathematicians. Phenomena investigated in hybrid systems with dry friction, processes of controlled heat transfer, obstacle problems and others can be described with the help of various differential inclusions, both linear and nonlinear. Fractional Evolution Equations and Inclusions is devoted to a rapidly developing area of the research for fractional evolution equations & inclusions and their applications to control theory. It studies Cauchy problems for fractional evolution equations, and fractional evolution inclusions with Hille-Yosida operators. It discusses control problems for systems governed by fractional evolution equations. Finally it provides an investigation of fractional stochastic evolution inclusions in Hilbert spaces. Front Cover ; Fractional Evolution Equations and Inclusions ; Copyright ; Table of Contents ; Preface; Chapter 1: Preliminaries; 1.1 Basic Facts and Notation ; 1.2 Fractional Integrals and Derivatives. 1.3 Semigroups and Almost Sectorial Operators 1.4 Spaces of Asymptotically Periodic Functions ; 1.5 Weak Compactness of Sets and Operators. 1.6 Multivalued Analysis1.7 Stochastic Process; Chapter 2: Fractional Evolution Equations; 2.1 Cauchy Problems; 2.2 Bounded Solutions on Real Axis ; 2.3 Notes and Remarks ; Chapter 3: Fractional Evolution Inclusions With Hille-yosida Operators; 3.1 Existence of Integral Solutions. 3.2 Topological Structure of Solution Sets 3.3 Notes and Remarks ; Chapter 4: Fractional Control Systems ; 4.1 Existence and Optimal Control ; 4.2 Optimal Feedback Control; 4.3 Controllability; 4.4 Approximate Controllability. 4.5 Topological Structure of Solution Sets 4.6 Notes and Remarks ; Chapter 5: Fractional Stochastic Evolution Inclusions; 5.1 Existence of Mild Solutions. Evolution equations. Differential inclusions. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Differential inclusions. fast (OCoLC)fst00893493 Evolution equations. fast (OCoLC)fst00917332 Electronic books. Print version: Zhou, Yong. Fractional Evolution Equations and Inclusions : Analysis and Control. San Diego : Elsevier Science, �2016 9780128042779 ScienceDirect http://www.sciencedirect.com/science/book/9780128042779 247285 247285